Abstract: This paper deals with the design of a nonlinear state observer for parameters within the gas transfer part of a fuel cell stack and its implementation on a small-scale embedded system. The fuel cell stack is of a proton exchange membrane type, with parameters specific to vehicle applications. The observer is afterwards applied on a small scale embedded board. In order to validate the embedded observer, a real time hardware in the loop testing is done using a co-simulation between the embedded observer and the professional simulation software AMESim, linked with Simulink on a Windows platform. To act upon the nonlinear character of the system, a Takagi-Sugeno approach is implemented, where the premise variables are unmeasurable. The procedure applies Lyapunov stability theory and by demanding bounded stability instead of asymptotic one, the algorithm manages to eliminate the need for Lipschitz constants.

The Hydrogen Fuel Cell systems have spurred interest in the last decade, despite the still high production cost, because of their elevated efficiency, reduced pollution level and the targeted independence from fossil fuels. Amongst different types of Fuel Cells (FC) like solid oxide or alkaline ones [1], the proton exchange membrane (P.E.M.) type [2] stands out, because of its low working temperature, and proves to be best suited for vehicle applications. In electrical vehicles, the energy storage plays one of the most important roles [3], so the research on Fuel Cells will boost the acceptance of electrical vehicles as well. Therefore, it directly competes with batteries which have been developing continuously for many years, yet prove inferior in some aspects to hydrogen technology as shown in [4], both as weight per storage capacity and energy density; these represent two important factors, that add to the slow recharge rate of a battery.

The Fuel Cells are small scaled devices therefore the development of virtual sensors would reduce the price. Also, a state observer may be used for diagnostics [5]. The majority of the papers that take into account the dynamics and not only the static models of FCs, focus only upon the electrical part of the fuel cell ignoring the auxiliary components [6] or treating just the compressor separately [7]. Nevertheless, papers such as [8], have to be mentioned as a thorough review upon all the components used so far. Indeed, for the more general case of system diagnosis, we find also many alternative approaches to model based techniques (for which a good review is [9]): experimental (ex: impedance spectroscopy [10], neuro-fuzzy techniques). As there is still no standardization in different existing types of FCs, a functional model would be easier to adapt to any particular case instead of experimental approaches that require extensive training data. Also model based approaches [11], [12] have the potential to give fast response to time variations, therefore being very efficient for on-line diagnosis [13] as well as control [14]. Of course one has to mention the greatest inconvenient of model based techniques that is the difficulty in parameter estimation. The state observer acts as a virtual sensors and it is designed to estimate cathode and anode pressures and mass flows of oxygen and hydrogen which are generally not measured. The mass flow rates of reactant gases play a pivotal role in the reliable and efficient operation of FCS.

For the design of the nonlinear observer, a Takagi-Sugeno (TS) representation has been chosen [15],[16]. This method can be found in literature, acting upon different types of industrial processes [17]. This approach has an advantage over other nonlinear ones in that there is no need for many assumptions regarding the form of the state space model, it has a structured form, it is easy to implement numerically and it also allows a parallel to linear techniques to be drawn. The construction of state observers based on TS representation has been in a continuous augmentation in the last period. Although many papers consider the premise variables measurable [19], this case in many practical applications is unfortunately unattainable. Among those who have tackled the issue of unmeasurable premise variables, one can cite [18].

It is useful to adopt the use of simulation software to replace the real system in the first hardware in the loop testing stage. For this, AMESim has been chosen [20]. Also, in the last years, small scaled embedded systems have become more and more accessible.

We can distinguish three classes:

Microcontroller (based boards) as Arduino boards;

FPGA which are good for parallel computing;

Processor based: as Raspberry PI, Beagle board, that act like small computers.

Each of them has certain advantages and disadvantages. In this article the authors have adopted the use of an Arduino Due board, and the development procedure with the hardware in the loop testing being described in [21].

The paper is organized as follows. Second section develops upon the Fuel Cell model. It is followed by a description of the TS representation and nonlinear observer design in the section III. Afterwards, in the fourth section, the embedded platform is described as well as the hardware in the loop (HIL) validation mechanism. The paper ends with results in section V respectively conclusions in section VI.

MATRAJI, I., S. LAGHROUCHE, M. WACK, Cascade Control of the Moto-Compressor of a PEM Fuel Cell via Second Order Sliding Mode, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference, December 2011, pp.633-638.